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Tuesday, January 26, 2010


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Suppose some person has a genuine, meaningful belief in the Trinity only if the meaning of the belief is not merely roundabout and derivative (e.g., "I believe in the Trinity in the sense the council fathers ascribed to it.").

(I am not sure about that conditional above, though. Similarly, I am not sure that it is absurd to claim that some proper name N's sense /decriptive content/ is merely derivative: e.g., the one who was named as "N.")

Suppose further the person believes in the Trinity, at least implicitly, in the following sense:

a) The Father is numerically distinct from the Son.
b) The Son is numerically distinct from the Holy Ghost.
c) The Father is numerically distinct from the Holy Ghost.
d) The Father is God.
e) The Son is God.
f) The Holy Ghost is God.
g) The "is" in the last three propositions is not the "is" of numerical identity, but of some other kind of identity.

Now, does the given person have to SPECIFY the kind in order to have a genuine, non-roundabout, epistemically possible belief in the Trinity in the sense of the conjunction (a)--(g)? I don't see that.

And would YOU have to? I do not see that either.

I'm sorry if you have addressed such questions elsewhere.


As for medieval philosophy as a "substance" abuse. Cf. Ramsey, Foundations of Mathematics, 1931, p. 269: "The chief danger to our philosophy, apart from laziness and woolliness, is scholasticism, the essence of which is treating what is vague as if it were precise and trying to fit it into an exact logical category." The problem is not one of the medievals only. Yet, even some (neo)(neo)scholastics are aware of the danger of "scholasticism": they do not give up the search for exactness (within the limits of the subject matter they explore) and try to come up with meticulous definitions of basic terms.

Maybe (g) is not good enough, so I suggest:

(g') The "is" in (d)--(f) is not the "is" of: numerical identity (like in "Cicero is Tully."), predication (like in "Socrates is wise."), accidental sameness (like in "Athena is bronze."), existence (like in "God is."); but of some other kind of identity.

Maybe even some other unsuitable kinds of identity and of "is" should mentioned, too.

Of course, here's a natural objection: If (g') holds, then "is" in (d)--(f) is bereft of any sense. Why? Because, so far, there seems to be no remaining sense of the "is" which the supposed believer could specify, explicate or define. The believer can reply that he does entertain the other, suitable sense of the "is," even if he is not able to specify, explicate or define it. Well, that is possible, I guess, but at the same time, I admit, dialectically ad didactically impotent: the communication stops, the believer just is not able to mediate his alleged sense of the other, suitable "is" to Bill.

Dear Bill,

let me say for the beginning that whereas I believe that understanding _how_ Trinity is possible is difficult (strictly speaking, according to the Catholic faith, imposible), the way how to grasp _that_ it is not evidently self-contradictory (and therefore epistemically possible) is quite easy, once certain distinctions are grasped.

The key is distinguishing two notions which BOTH are intuitively associated with the philosophical concept of individual substance, but in case of Trinity they are separated. Once you see that it is NOT epistemically evident that they CANNOT be separated, you have the room for the possibility of the Trinity. Solving various counterarguments i then but a technical matter.

The concepts are these two: 1) Individuality 2) Suppositality.

1) Individuality. Individuality is something that nowadays should have been called "un-instantiability" or "un-exemplifiability" - scholastically speaking, the property of not being capable of further division into "subjective parts"; that is, something of which the original thing would be truly predicated as a whole. "man" is not an individual, because it can be "divided into" Socrates, Plato etc. Socrates is an individual, because there cannot be any instances of Socrates. Individuality is thus incommunicability to subordianted instances.

2) Suppositality is the property of _absolute incommunicability_, that is, not just incommunicability to many individual instances, but also incommunicability to a subject (or supposit). Plato's humanity is individual, as it is not instantiable, but it is NOT a supposit: it does not have suppositality, because it is COMMUNICATED TO a supposit (viz. Plato). But Plato is absolutely incommunicable, it IS a supposit, an ultimate subject in the ontological as well as logical order.

Now it is important to understand that individuality does not of itself imply suppositality. You can imagine the two properties as two degrees of completion of a real individual supposit: "first" (logically, not temporally) there comes the individuality which "contracts" the common nature to an individual nature, it works like a differentia. Then there comes the "suppositality", which is the ultimate "seal of completion" of the entire being, it turns the individual nature into a true individual supposit, the real thing to which properties, actions and passions are ascribed.

Now: the entire "trick" in case of the Trinity is that whereas "usually" there is just one suppositality to go with a given individuality, that is, individual natures are usually of such a kind that they can subsist only once, only in one supposit, the divine nature requires three supposita, three suppositalities to "finish" it. We may never know why, but we cannot say there is any contradiction in the entire notion.

There is one thing that can be a problem for a post-Fregean thinker: modern logicians tend to confound precisely the two differrent relations I have distinguished: namely, the relation UNIVERSAL-INDIVIDUAL, and the relation PROPERTY(FORM)-SUBJECT. It is important to see that these two do not coincide. The former is the relation of instantiation, the latter is the relation of inherence (of a form in a subject). We have even different linguistic means to express these two different relations: the FORM-SUBJECT(SUPPOSIT) distinction is captured by means of the distinction between concrete and abstract nouns, whereas the UNIVERSAL-INDIVIDUAL distinction is captured by means of the distinction of proper common nouns. The moderns tend to confound universality and abstractness, which is a mistake: an "abstract" thing can be individual (Socrates-ness, Socrate's humanity).

I hope this hepls,



Thanks for your comments, which are interesting and helpful. >>Now, does the given person have to SPECIFY the kind in order to have a genuine, non-roundabout, epistemically possible belief in the Trinity in the sense of the conjunction (a)--(g)? I don't see that.<<

In other words, does the person have to specify the exact sense of 'is' in (d)-(f)? I should think so, especially since, in your third comment, you rule out the standard readings of 'is': identity, predication, existence, composition (what you call accidental sameness). You might also want to exclude the veritative 'is' and the locative 'is.' And possibly other uses of 'is' that I have not cataloged. Being is said in many ways! (as old Aristotle said)

To understand the Trinity doctrine, I have to understand among other things what 'The Father is God' means. But if you have excluded every definite meaning of 'is,' then I won't know what exact proposition I would be believing if I were to believe that the Father is God. Suppose I wrote 'The Father iz God.' That is meaningless and expresses no proposition. Similarly if I say 'The Father is God in a sense of 'is' that no one has ever specified.' There is just no proposition there for my mind to grab onto and either affirm or deny.

Dear Dr Vallicella,

I’m honored to receive your reply. In some points my response has been anticipated by Lukas Novak, but I’ll answer your post in some detail nonetheless. Please forgive the length.

I’m sorry that you think I was equivocating. Equivocation is a confusion of terms, whereas I was trying to clarify. My original comment was not meant to “explain how the doctrine could be true,” as you write, but only to try to clarify what the doctrine is by pointing out a fundamental distinction (as given, for instance, by Thomas Aquinas in Summa theologiae I. q.29 a.2). As I wrote on my own blog, “This doctrine is not a proposition or set of propositions existing in a vacuum, so that one can examine, e.g. the Athanasian Creed all by itself without reference to how it is and has been understood by those espousing it; otherwise one's critique runs the risk of having no bearing on the actual doctrine as affirmed and believed. Otherwise it will be nothing but an analysis of the residue of a set of propositions after one has run them through the alchemical transformations of one's own modern hermeneutical apparatus.” I think that this is happening again in your latest post.

According to you: You write that God is a nature, and that this nature is thrice instantiated in the Father, the Son, and the Holy Ghost. But you may notice that I never wrote any such thing. It is clear that you’ve taken the word “nature” in the wrong sense, and read “instantiation” into it when this is doctrinallly inappropriate. Again, you write, Your talk of instantiation suggests that God is a multiply instantiable entity whose instances are F, S, HG.

But I very much wish to deny this. It is central to monotheism that there is only one instance of the divine nature, and so whatever the multiplication of persons in God may be taken to mean, it cannot mean that there is more than one instance of God or individual God, which as you rightly point out compromises monotheism. As St Bonaventure says (In Sent. I.2.1): “It is impossible for there to be several gods, and if the meaning of the word ‘God’ is correctly received it is not only impossible but even unintelligible.”

So your use of “nature” to mean “multiply instantiable entity” suggests that the divine nature is a universal which is individuated in three instances. But the divine nature is not a universal, apt to be applied to or predicated of many, but a “form” which is singular by necessity. Theologians explain this necessity because of God’s simplicity (in order for a universal to be multiply instantiated it has to enter into composition with some individuating factors, but the divine nature is neither composible nor composed), God’s infinity (the divine nature is without limitation, but every case of instantiation involves a delimitation of one instance from all others), and so forth. Duns Scotus writes (in Reportatio I-A 2.3.3), “Whatever is of itself just a ‘this’ cannot possibly be multiplied, but whatever exists in the divine that is of one sort, is just of itself ‘this’ [i.e. is individual per se]”.

Every orthodox theologian, therefore, denies that in the Trinitarian productions – the generation of the Son by the Father or the spiration of the Holy Ghost by the Father and the Son – God produces another God, precisely because the divine nature cannot be multiplied. Again, Scotus (Reportatio I-A 5.1.1): “The essence neither procreates nor is procreated, and all the arguments that I find why it does not generate really come down to this. If this thing generates, then it procreates a real thing distinct from this essence. For no real thing generates itself. Therefore, it procreates some real thing that is not in the divine nature, because intrinsically there is no diversity there . . .”

If the divine nature were multiplied, there would be a plurality of Gods, and so a plurality of divine existences, operations, etc. But it’s intrinsic to the doctrine of the Trinity that the being or existence of the Father and the Son is one being. The operation whereby God creates the world is one operation, equally belonging to all three persons, not three cooperative activites. The Father, Son, and Holy Ghost are not one God because they are each a (different) instance of the divine nature, but because they are each the same instance of the divine nature. Scotus once more (Reportato I-A 4.2): God is Father, Son, and Holy Ghost “by a singularity which is shared, by which ‘this God’ is common to all three. And a singularity or haecceity similar to this is not to be found in creatures, because in creatures nothing is a ‘this’ except by the ultimate haecceity, which is completely incapable of being shared.”

That is, for creatures a supposit or hypostasis is only distinguished from another one of the same nature by the multiplication of the nature through an individuating difference. “Humanity” is not a singular individual nature by itself, but only by an additional instantiating factor. But “deity” is a singular individual nature by itself.

This is why the divine persons are said to be distinguished from one another only by their relations of origin. The Son has the very same deity that the Father has, which means he shares every single attribute belonging to the Father, except Paternity. In begetting the Father communicates his numerically identical essence and existence to the Son, and fails to communicate only his ingeneracy, the fact that he is unbegotten. St Bonaventure writes (In Sent. Whatever the Son has, he has either freom himself or from another; but he has deity, and not from himself, for then he would be unbegotten, therefore he has it from another.”

So there is no individuting factor in the three divine Persons except their relations of origin, and these relations are within the single divine nature or essence rather than multiplications of it. Paternity and Filiation are ways in which the one God is related to himself. The divine persons as distinct from one another have only relative subsistence, as opposed to the absolute subsistence of the divine nature. Again, this is contrast to the state of things we’re familiar with, in which for there to be many human persons there have to be many humanities. St Bonaventure once more (In Sent. “Father and Son and Holy Ghost are united in this name ‘God’, not from diverse causes [of individuality] but by reason of one deity or essence. [In contrast] there is a union of diverse causes, for example, when Peter and John are united in ‘man’, but by reason of diverse instances of humanity, because the humanity of Peter is one thing while that of John is another. . . . but Father and Son and Holy Spirit are united in one deity or essence but are distinct by reason of the plurality of persons.”

Any nature except the divine nature is a “multiply instantiable entity”, not individual through itself, and so the multiplication of hypostases, persons, or supposits requires the multiplication of the nature through some individuating factor in addition to the essence, whereby John’s humanity is specifically identical to but numerically distinct from Peter’s humanity. But, as I said before, the divine nature is necessarily individual through itself, and so in the multiplication of supposits in God the nature “deity” remains numerically as well as specifically identical, and the supposits or person are only distinct through their constituting relations.

I hope all this is more explanatory without being too repetitive.


I didn't realize your comment box doesn't accept html. I hope my comments will still be intelligible without the italics. I'm posting this reply at my own blog as well.


You write, "According to you: 'You write that God is a nature, and that this nature is thrice instantiated in the Father, the Son, and the Holy Ghost.' But you may notice that I never wrote any such thing. It is clear that you’ve taken the word “nature” in the wrong sense, and read “instantiation” into it when this is doctrinallly inappropriate. Again, you write, Your talk of instantiation suggests that God is a multiply instantiable entity whose instances are F, S, HG.

Seems to me I paraphrased you quite accurately. YOU used the word 'instantiated.' Here are your exact words: "in the case of the Trinity there is one divine nature (God) instantiated in three hypostases (Father and Son and Holy Spirit);" You are saying that the divine nature, which is God, is instantiated.

I have the strong impression that discussing this with you further will not lead to anything worthwhile.

Dear Dr Vallicella,

I wrote: "there is one divine nature (God) instantiated in three hypostases"

You wrote: "this nature is thrice instantiated in the Father, the Son, and the Holy Ghost"

These statements are not identical, and the latter does not paraphrase the former quite accurately.

The crucial point is that the divine nature is instantiated *once* in three persons, not *thrice*. The plurality of persons does not imply or require a plurality of instantiations.

I think that the rest of my comment makes this clear. But your concluding sentence makes me suspect that you didn't bother to read it, assuming that I lapsed into incoherence at the beginning. I would be sorry if this were the case.


Thanks for your comment. You distinguish, reasonably enough, among common nature, instance of a common nature, and supposit. Thus the common nature humanity has as an instance Socrates' humanity. But this instance (property-instance, trope in other jargons) is distinct from Socrates and inheres in him. Accordingly, there are two relations, instantiation and inherence. Particular instances of a common nature instantiate that nature, but these particular instances inhere in supposits. Individuals are either instances of a common nature (e.g. Plato's humanity) or supposits. An instance is communicable to the supposit of which it is the instance, but supposits are absolutely incommunicable. Every supposit is an individual, but not every individual is a supposit.

But I am having trouble applying this scheme, which I am not at the moment questioning, to the Trinity. First of all, in the case of God there is no common nature. God is absolutely unique. He is not in a genus as Aquinas says. If there is no common nature, then I wonder what an instance of this common nature would be. If an instance is an instance of a common nature, and there is no common nature, then there is no instance. You seem to be saying that God is an individualized nature, and that this nature has three supposits, the F, S, and HG.

So your claim is that God is to the three Persons as individual nature to three supposits. But now the problem is to explain how the individual nature (God) can have three numerically distinct supposits while remaining an individual nature. Given that the Persons are distinct among themselves, the Father's divinity, the Son's divinity, and the Holy Ghost's divinity must be distinct among themselves. On your approach the individual nature becomes a universal (a multiply exemplifiable item) and ceases being an individual.

Unlike Sullivan, you have addressed the problem of the logical coherence of the Trinity doctrine, but I don't see that you have solves it. Note that I am not objecting to your distinction between instance and supposit. That is a distinction even non-scholastic philosophers make, using different terminology. My point is that an instance cannot have more than one supposit on pain of ceasing to be an instance.

Dear dr. Vallicella,

I first apologise for having addressed you informally in my previous post...

I will try to answer your objections - two of them, as far as I can see - and then append some more explanation. Let me say that it is a delight to discuss the problem with someone with such a

First objection: There is no common nature in God.

I reply: First: I agree that God is absolutely unique; but that does not imply that there is no common nature in Him. I happen to agree rather with Scotus that there are concepts, the transcendentals, that are univocally predicable both of God and some or all created things. Thus, there are some "common aspects" in God, although God as God is unique.
Second: Even if I conceded the Thomist view that no concept is univocally common to God and anything else, and interpreted it so that every universal truly and completely predicable of God is unique to God, still it would be possible to distinguish the universal concept, say "God", and its unique instance, the God. There simply can be "individual" concepts, or universals of such a kind that they allow just one instance ("even prime" is of that kind, if we take numbers as individuals). So I don't see any problem here.
Third - even if I conceded that there were a problem in positing a pseudo-common concept of God, so what? In case of God, let there be just the individual nature, no common concept, no common nature, no relation of instantiation. But this is not something on which the trinitary doctrine hinged. What is necessary to understand is that the relation between the nature and the supposits/Persons is not that of instantiation, therefore, that the divine nature is not "common" to the Persons in the way universals are common to their instances. From the (correct) assumption that divine nature is not common as a universal you cannot conclude that it is not common as an individual nature in more supposits.

Your second objection: You write: "Given that the Persons are distinct among themselves, the Father's divinity, the Son's divinity, and the Holy Ghost's divinity must be distinct among themselves" - and conclude that this makes God's nature universal.

But I don't see how the quoted implication is warranted at all. Yes, the persons are distinct, because they are constituted through distinct suppositalities. But from that does not follow that there must be more than one divinity. Or at least not oviously at all. Therefore, so far no obvious inconsistence has been shown in the trinitary conception.

Let me try to offer some more explanation.

Note first that the suppositality does not have the power to multiply instances. It simply turns a nature into a supposit; from a nature capable of being received by a subject it makes a supposit incapable of that. Normally, natures are capale of only one such termination, but is there any contradiction in a nature being capable of (or even requiring) three of them?

Note second that the individual nature is very different from a common nature. A common nature is an abstraction, something that does not exist really (at least according to the sober, moderate-realist view :-)), its's numerical unity is merely intellect-made. But an individual nature is indeed something out there in the reality, its numerical unity is a real one. As such it is of itself incapable of further instantiation or division. On the other hand, it is not yet a "this one here" (to de ti), a concrete supposit. It is a real aspect of a supposit, but it is at least conceptually distinct from it. Properly, you cannot say that a nature acts, that it does this or that, that it has this or that (first-order) property. So you can never count a nature among supposits or vice versa.

Note third that you cannot use this (and similar) arguments to refute the Trinity: "it is contradictory that something one is identical to three distinct things". One has to be exact: one WHAT and three WHAT? It depends, what you are counting, whether individuals or supposits. There is just one individual but three supposits; and as long as you concede the distinction between individuality and suppositality, there is no ground to accept inferences from the one to the other (e.g., as you have it, multiplication of supposits -> multiplication of individual instances). Therefore, one and the same reality can be both one individual and three supposits, just like one and the same reality can be one game but 32 pieces (although the specific relations between the one and the many entities in the respectivre cases is different in each case).

Perhaps you say: but then one and the same thing both is and is not distinct from itself. I reply: yes, but in different respect, therefore no contradiction. Identity and distinction comes in kinds. There is identity and distinction based on individual unity, and another identity and distinction based on the unity of a supposit. The Trinity is not one as a supposit, but it is one as an individual. The Persons are distinct from each other as supposita, but are not distinct from each other as individuals, because they share their individual unity (rooted in one individual nature) but not supposital unity (due to three distinct suppositalities).

Well, I have written quite a lot; I suggest that in your reply you concentrate on the problem how does it follow from the fact that supposita are multiplied that instances are multiplied. If you can prove it, then trinitarianism fails. But I am quite confident you can't :-) For me, the problem is not "to explain how the individual nature (God) can have three numerically distinct supposits while remaining an individual nature", but to explain why this should be a problem at all :-)

Best regards,

Lukas Novak

Dr. Novak,

No need to apologize. It's a sort of dilemma: I don't like false familiarity, but I also don't like false formality. But it is no big deal. I got a laugh, though, out of this: "Let me say that it is a delight to discuss the problem with someone with such a"
which is a sort of complimentary *carte blanche.* I return the compliment.

You bring up a host of issues. My time is limited, but let me try to address at least one of your points.

Transcendentals and common natures. You mention the transcendentals (ens, verum, bonum, unum, etc.) As I understand it, these are so-called because they transcend genus-species classification. They abstract from quidditative content. Every being is one (unum), for example, no matter what genus it belongs to, no matter WHAT (quid) it is. Now I want to avoid if possible the question whether 'being' is univocally predicable of both God and creatures. That is a bone of contention, as I recall, between the Scotists and the Thomists. Though I am not a Thomist, my thinking on certain topics (existence mainly) has a Thomistic flavor. My point would be that common natures are distinct from transcendentals. In any case, I was not including the transcendentals within common natures. By 'common' I think you mean multiply exemplifiable or multiply instantiable. (I tend to use these two phrases interchageably.) If that is what you mean, then I would argue that God -- who you grant is absolutely unique -- cannot be an instance of a common nature. For if he were, then it would be possible that there be a second being, God*, who is also an instance of that nature. This, however, is impossible, because God is absolutely unique.

When I say that God is absolutely unique, I do not mean that God is one of a kind, or even that he is necessarily one of a kind; I mean that in God there is no real distinction between the divine nature and God. This is of course an entailment of the doctrine of divine simplicity (DDS). You may want to look at my Stanford Encylopedia of Philosophy entry on this topic: http://plato.stanford.edu/entries/divine-simplicity/

My point, then, is that with respect to God there is no real distinction between the common nature, divinity, and an instance of that nature. As a result, your ontological scheme, which makes sense in respect of creatures, does not apply to God.

Dr Novak writes,

"Second: Even if I conceded the Thomist view that no concept is univocally common to God and anything else, and interpreted it so that every universal truly and completely predicable of God is unique to God, still it would be possible to distinguish the universal concept, say "God", and its unique instance, the God. There simply can be "individual" concepts, or universals of such a kind that they allow just one instance ("even prime" is of that kind, if we take numbers as individuals). So I don't see any problem here."

This sound self-contradictory. 'Universal' just means multiply exemplifiable, and so it is self-contradictory to speak of "universals of such a kind that they allow just one instance."

I agree that the propery of being an even prime has exactly one instance, the number 2. For this very reason, this property cannot be called universal. It is not a one over many, or a one in many. Universal = repeatable. Particular = unrepeatable. Of course, you are free to use terms as you like, but if you diverge too far from 'standard' usage, people will not understand you.

Furthermore, even if there are haecceity-properties (H is an haecceity-property of x iff x has H, x has H in every possible world in which x exists, there is no y distinct from x that instantiates H in any world), God cannot instantiate such a property because of the divine simplicity.

More later.

Dr Novak,

The problem is to show how the following propositions are logically consistent:

a) The Father is numerically distinct from the Son.
b) The Son is numerically distinct from the Holy Ghost.
c) The Father is numerically distinct from the Holy Ghost.
d) The Father is God.
e) The Son is God.
f) The Holy Ghost is God.
g) There is only one God.

If the 'is' in (d)-(f) is the 'is' of identity, then a contradiction is easily derivable. Now your solution, in effect, is to understand (d)-(f) as follows:

d*) God (the individual divine nature) inheres in the Father
e*) God inheres in the Son
f*) God inheres in the Holy Ghost

Unfortunately, it is difficult to see how the last three propositions could all be true. If the individual divine nature inheres in three distinct supposita, then it is not individual but precisely common to these three. You are saying in effect that the individual nature both is and is not an individual nature.

Dear dr. Vallicella,

I suggest to drop the problem concerning the universality of God's nature. I concede that if you define a universal as something multiply instantiable, then "God" is not a universal. On the other hand, I can't see how God's simplicity precludes the possibility of God's instantiating a "haecceity-property". The entire problem however has no bearing on the probelm of Trinity, so I suggest we drop it.

Now to the main problem. In your previous post you backed your claim that Trinitarianism (shorthand T) is inconsistent by the following crucial assumption: "Given that the Persons are distinct among themselves, the Father's divinity, the Son's divinity, and the Holy Ghost's divinity must be distinct among themselves." I have rejected this implication, but you now don't seem to make an attempt to prove it. It seems to me then that that particular ways of proving a manifest contradiction in T failed.

Now you present a bit different argument.

I am not entirely happy with your formulations "God inheres in the Father" etc., but I will accept them for the moment, further qualifications would mislead us.

The crux of your argument are your two concluding sentences: "If the individual divine nature inheres in three distinct supposita, then it is not individual but precisely common to these three. You are saying in effect that the individual nature both is and is not an individual nature."

Let me comment on them.

First: The burden of proof is on the party who is claiming that there is manifest contradiction in T. It is not necessary to be able to "see HOW T can be true"; as long as there is not a clear deductive valid argument to show there is a contradiction in T, there is no reason to think it cannot be true.

Second: From that follows that T could be claimed manifestly self-contradictory only if your 2 concluding sentences were manifestly true. But they don't seem to be so, they seem to be asserted quite gratis.

Now I distinguish the meaning of "common":
1) CommonU - Common as a universal
2) CommonO - Common in other ways

x is common as a universal with regard to y,z,... iff y,z,... are instances of x.

x is common some other way with regard to y,z,... iff x is in some way related to y,z,... as one to many, but not as a universal to its instances.

Thus two students can have a flat in common, without the flat being universal for that; two politicians can have a common goal, or two people a common individual ancestor. So not all kinds of community preclude individuality.

Now I concede that it follows that if divine nature is one inhering in three supposits, it is commonO to them. But that does not imply that it is commonU to them. As I have said, suppositality has no power to instantiate, there is no reason to assume that if X takes on suppositality, an instance of X results. Seen the other way around, in order for X to be able to take on suppositality, it must "already" be individual. So it is incapable of being instantiated anyway. You said you concede the distinction between instantiation and inherence. How can you still maintain that manifold inherence implies manifold instantiation?

Perhaps the problem is that you have a "platonic" conception of universals? In that case, the distinction between community of universality and other kinds of communities may seem blurred to you, because in both cases there is something that is really and actually one, common to many.

Perhaps you can, with a grain of salt, understand the classical conception of T as the only real instance of a "platonic" universal being common to many. But remember that the classics would never call this true universality, because a true universal is instantiated in many numerically distinct natures or essences, and is thus really "divided" and "multiplied" (Socrates and Plato are not one man but two men). This is not the case with God - there are multiple persons, but not multiple God's.

Best regards,


I. The propositions listed below are formally inconsistent: i.e., it does not matter which names, predicates, modified predicates we substitute for the non-logical terms occurring in these propositions, the resulting set of propositions will yield a contradiction. Therefore, not all the propositions listed below can be true: one or more must be false. I shall call the set of propositions listed below the Trinitarian-Inconsistent-Set, or (TIS) for short.

1) There is exactly one God or exactly one entity exemplifies Godhood;
2) There are exactly three numerically distinct divine-persons;
3) The Father is a divine-person;
4) The Son is a divine-person;
5) The Holy-Spirit is a divine-person.
P1) Whatever is a divine-person is divine; or whatever exemplifies divine-personhood exemplifies divinity;
P2) The set of entities that exemplify divinity is identical to the set of entities which exemplifies Godhood;
P3) Whatever exemplifies Godhood is numerically identical to God.

II. The most natural interpretation of the ‘is’ in (3), (4), and (5) is as exemplification. In (1), the phrase ‘exactly one’ secures uniqueness: i.e., it says that there is an x such that x is numerically identical to God and if for every entity y, if y is identical to God, then x is numerically identical to y. Or alternatively, there is an x such that x exemplifies Godhood and for every y that exemplifies Godhood, x is numerically identical to y. The phrase ‘exactly three’ in (2) secures the existence of at least, but no more than, three numerically distinct divine-persons.

III. Since the set of propositions in TIS are formally inconsistent, we must reject at least one of them. What are the constraints that should guide us in selecting which proposition(s) should be rejected? First, we have orthodoxy: no proposition that is directly required by orthodoxy can be rejected. Therefore, we have the following constraint:

(C1) All propositions that are required by orthodoxy must be retained.

Second, we have logical considerations. Proposition that are required by logic must be retained or not violated. Propositions that are not required by logical considerations can be abandoned so far as logic is concerned. So we have the following logical constraint:

(C2) All propositions that are required by logic must be retained and propositions that are not required by logic can be abandoned.

IV. For the sake of the Trinitarian doctrine it better not turn out that (C1) and (C2) collide over one or more of the propositions above: i.e., it better not be the case that while logic requires retaining/rejecting one of the propositions, orthodoxy demands the opposite. For if there is a collision between orthodoxy and logic, then the Trinitarian doctrine cannot be made intelligible. In order to avoid such a collision, some of the propositions above need to be interpreted in a manner that conforms to orthodoxy and yet the set of them all is not formally inconsistent.

V. Propositions (P3) and (P2) are unchallengeable. (P3) secures monotheism and (P2) asserts that the property of divinity is identical to the property of Godhood. Propositions (1)-(5) each states some tenet of orthodoxy. While there may be room to negotiate about the interpretation of one or the other, it seems that such approaches end up in the same place that TIS itself leads: i.e., they either flout logic or orthodoxy.

VI. What about (P1)? It is this proposition that Bill frequently uses in order to show either that a given interpretation leads to tritheism, which flouts the orthodox creed of monotheism and hence violates(C1), or to a contradiction, which flouts logic and violates (C2). (P1) says that the property of divine-personhood is linked to the property of divinity such that whatever has the former has the later. Thus, since each of the three persons (F, S, and HS) has the property of divine-personhood, it is (P1) that certifies Bill’s inferences that, therefore, each of the three persons has the property of divinity. Once this conclusion is obtained, there is no escape from deriving tritheism. So Bill’s argument relies heavily on (P1).

VII. One way to block Bill’s strategy is to deny (P1). TIS minus (P1); i.e., (1)-(5), (P2), and (P3), is not formally inconsistent: we cannot derive from this set that each of the persons is divine and, therefore, that each of the persons is God. Hence, no tritheism follows. But on what ground should one reject (P1)? While the advocates of the intelligibility of the Trinitarian doctrine will ultimately have to address this question, they need not do so at this stage. Since it is Bill who employs (P1), he should provide grounds for accepting it. So the question presently is this: What grounds can Bill offer in order to justify accepting (P1) and including it in TIS?

VIII. Can Bill point to an orthodox creed that requires the inclusion of (P1) in TIS? If so, let us make this creed explicit. Alternatively, perhaps Bill thinks that the inclusion of (P1) in TIS is required by some logical or quasi-logical considerations? If so, let us put such reasons on the table and examine them.

IX. I myself think that (P1) is false. But I shall refrain at this stage from arguing this point and let Bill have his say first.


My man! You've done an excellent job of laying out the constraints on a solution to the Trinitarian consistency problem. We must try to solve the problem without falling into heresy (Arianism, Sabellianism, etc.)and also without abandoning standard logic, where standard logic requires absolute identity (as opposed to sortal-relative identity). Only if we cannot solve the problem within these constraints will we have a reason to engage in theological or logical innovation.

To put it graphically, we want to see if we can avoid a collision between the commitments of Christian orthodoxy and standard logic. But if there is a collision, which ought to be the first to give way? It seems to me that logic has veto-power over theology, but some will disagree. I take it that fideism and irrationalism are off the table, at least for now.

Now where I disagree. Your TIS I find tendentious and question-begging. You have assumed that in 'The Father is God' the 'is' must be read as an 'is' of predication. But that is quite a distance away from the creedal formulations. Here is a simpler and more accurate depiction of the problem that stays close to the Athanasian Creed (I borrow this from Brower and Rea with slight modifications):

1. Monotheism: There is exactly one God.
2. Divinity of Persons: The Father is God, the Son is God, the Holy Spirit is God.
3. Distinctness of Persons: The Father is not the Son, and the Holy Spirit is not the Father or the Son.

We agree that if 'The Father is God' is an identity sentence, then a contradiction can be derived. So you think the 'is' must be read as an 'is' of predication. But that doesn't follow, since it could be read as an 'is' of composition as Brower and Rea do. My point is that your formulation above is tendentious and question-begging.

My earlier argument was as follows. Suppose we replace the sentence in question with 'The Father is divine' where 'is' is the 'is' of predication and 'divine' is a predicate. Corresponding to 'is' is the relation or quasi-relation of instantiation (exemplification), and corresponding to the predicate is the property of being divine. That property is the multiply exemplifiable property of being a god. Now if the Father exemplifies this property, then the Father is a god. After all, 'x exemplifies F-ness' is equivalent to 'x is an F.' The same goes for the Son and the HS. Now if each person is a god, then there are three gods because the persons are distinct. Thus we arrive at the heresy of tritheism.

I don't understand why you don't accept this argument.

Are you assuming that divinity is the haecceity-property of being identical to God, where 'God' is a proper name? That property is of course not multiply exemplifiable, unlike the property of being a god.

Note that if you read 'The Father is God' as 'The Father exemplifies the property of being identical to God' then you haven't accomplished anything: the contradiction can be derived as before.

You need to clarify your reason for disagreeing with me.


Let me just focus on one point. My understanding is that the orthodoxy claim is "The Father is a divine-person"; the same goes for the Son and the Holy Spirit. It is from this proposition that one then needs to derive that "The Father is divine", and then from this your argument kicks in. You seem to have skipped the step involving the predicate 'divine-person' and you went directly to 'divine'. Now, if I am wrong about this, then I have nothing to stand on. But if I am right, then you employ (P1) as I have stated in the above post, and you need to justify this principle.


You have the Brower and Rea paper. On the second page there is a quotation from the Athanasian Creed. We do not find the sentence "The Father is a divine-person" but we do find "The Father is God." I am not sure what you meaning by your sentence with the hyphen. You seem to think I need to justify the inference from "The Father is a divine-person" to "The Father is divine." But I am not inferring the second sentence from the first. The second sentence is a proposed reading of "The Father is God," a reading that is proposed as a way to avoid inconsistency. And it does avoid inconsistency, but at a price, namely tritheism.

As I recall, you made the point, which is correct, that from 'Peter is a short basket ball player' one cannot validly infer 'Peter is short.' Apparently you think that a divine person needn't be divine.

Why? I don't get it. 'Short' is relational. One can always ask: compared to what? 'Divine' is not relational.

Dr Novak,

I hope to respond tomorrow. Thank you for your comments.

Dr Novak,

Some questions:
1. Are you a Scotist? If not, which brand of scholastic philosophy do you represent?
2. Does Scotus accept the doctrine of divine simplicity (DDS)? A simple God admits of no metaphysical composition whereas Trinitarian doctrine does seem to imply such composition. Therefore DDS does seem relevant to the overall problem.
3. Do you use the Latin 'suppositum' as the equivalent of the Greek 'hypostasis'?
4. Can you provide a rigorous definition of 'suppositum' of the form 'X is a suppositum if and only if _____________'?
5. Your view seems to be that the individual nature *Socrates' humanity* inheres in S's suppositum. Is that right? Is a suppositum then something like a a bare particular (Gustav Bergmann) or a thin particular (David Armstrong)? What exactly is the relation among these three: Socrates, Socrates' suppositum, the individual nature *Socrates' humanity*?

Dear dr. Vallicella,

here are replies to your questions:

Ad 1) I wonder if I qualify as a Scotist... I accept some scotistic theses ("essentialism" in Gilson's sense, univocity of being, libertarianism, formal principle of individuation) and reject or doubt others (formal distinction, forma corporeitatis, intrinsic modes as primary contractives of being...). I think I am located somewhere in beween Scotism, post-Cajetan thomism and Suárez.

Ad 2) Difficult to answer: Scotus certainly believes that God is absolutely simple, but at the same time has no problem with the Trinity at all; so if accepting trinitarianism implies departue from DDS, then Scotus (and any Christian) does not accept DDS. Scotus also believes that certain formal non-identity in God is compatible with His absolute simplicity.

Ad 3) "Hypostasis" in this sense usually means "suppositum endowed with rational nature". So "suppositum" is broader. But with regard to Triniy, the two terms coincide extensionally.

Ad 4) X is a suppositum iff X is something endowed with individual nature and suppositality, that is, X is both uninstantiable and incommunicable to a subject (and not a part nor an aggregate).

Ad 5) It is better said that Socratess' humanity inheres in Socrates, who is a suppositum. Suppositum is not a bare or thin particular. If there were bare particulars, they would probably be classified as supposita, but clasically supposita are not considered to be "thin" or "bare" - they have their rather "thick" essences or natures de re necessarily. Socrates is identical to Socrates' suppositum. Socrates' humanity inheres in Socrates and is a metaphysical constituent of Socrates. Socrates' humanity plus his suppositality makes up Socrates. Neither Socrates' humanity nor his suppositality are entities in their own right, they are just aspects or metaphysical constituents of Socrates. So I use "inhere" here as _not_ implying any particular kind of distinctin between the nature and the suppositum.

Dear participants in discussion,

I would like to make some comments concerning the "TIS" and the meaning of some terms used to speak about the Trinity. I am afraid there are several ambiguities that blurr the discussion.

I) the term "God" is ambiguous in its reference. It can mean at least 3 different things:

a) the divine nature;
("Godhead", divinity)
b) a supposit endowed with divine nature or "a supposit that is God";
(a divine person)
c) A being having divine nature.
(the Holy Trinity)

When we say "There is just one God", we use the meaning a) or c): there is just one divine nature and just one being that is divine (because beings are counted according to the number of individual essences or natures). But we don't mean to say that "there is just one supposit that is God". This is clearly false, on trinitarian assumptions.

Now what I want to say: As long as "There are three Gods" is understood as formally implied by "There are three numerically distinct supposita, each of them being God", it must be so understood that "God" in "there are three Gods" has the meaning (b) - otherwise it is not implied by the latter sentence. But in this reading it is correct and orthodox, because in this way the sentence does NOT express the plurality of natures, but only of supposits. The expression "There are three Gods" is banned only because the plural "Gods" is understood as authomatically (semantic rule, not logical implication) conferring multiplication on God's nature itself. But the meaning "There are three distinct from one another, each of them being God" is orthodox, and trinitarianism IS "tritheist" in this sense.

II) "Entity": another ambiguous word. It can either mean "a supposit", or "a being". Note that in God the trinitarians believe that one being (i.e. something constituted by one individual nature) exists as three supposita. How many "entities" are there?

So, according to various senses of "God" and "entity", there are at least 6 different meanings of

1): There is exactly one God or exactly one entity exemplifies Godhood;

some of them orthodox, some not; and also various meanings of P1, some orthodox, some not.

III) The "distinction" of divine persons from one another can be understood too strongly. In the classical conception, it is not meant to imply that they have nothing in common, that they are in no way identical. In fact, they have evrything in common except their suppositalities or personhoods. They are distinct merely _as persons_ or suppostita.

IV) The notion of divine simplicity. Obviously the classical conception does not understand is so strongly that it would be at variance with trinitarianism. The doctrine of divine simplicity describes the essential nature of God, that is, it applies on Him with regard to his essence or nature. The divine simplicity is a philosophical conclusion concerning God, and philosophy can only "see" divine essence, which it finds to be absolutely simple. The trinity of persons is something that ex definitione has no bearing on divine essence, and it is something that is philosophically "invisible". Therefore, if trinitarianism is consistent at all, it is not at variance with the doctrine of divine simplicity, since it "ex definitione", as it were, places itself without the area of the philosophically attainable knowledge of God, to which the doctrine of divine simplicity is confined. Any interpretation of the trinitarian doctrine that would understand it as compromising the simplicity of divine nature or essence would be a wrong interpretation of the trinitarian doctrine in the first place. It is an article of (the Catholic) faith that the Trinity is a "mysterium stricte dictum", that is, something absolutely out of reach of natural reasoning. (Wich BTW is something very different from saying that it is self-contradictory or meaningless.)

Best regards,


Dear dr. Vallicella,

just now I become aware that must to have missed your post from January 27, 2010 at 05:12 PM. I apologise, I kind of struggle with the system - e.g. I never succeed in posting my text after having previewed it. I have to copy it, reload the page anew and insert it again...

I am quite embarrassed concerning the "complimentary carte blanche". I wanted to write "...such a good understanding for the opponent's way of thinking". Perhaps I never finished the sentence, or it got scrambled during the copy-n-paste process... Good luck you've such a good sense of humour....

Please take the following remarks just as an explanation of my position to be perhaps better able to understand what I mean, please don't feel to be bound to reply.

Regarding the transcendentals, I suppose that it is a merely tangential matter, but I don't think they have no quidditative content. For me, "being" is just the highest genus. I also don't have any problem with the common predicates like "good", "wise" etc. applying univocally to God and creatures. My position is the moredarate-realist one, similar to Oppy's. There are "properties-in-things" which are always individual and multiplied, and there are concepts of these properties, say "properties-as-meanings". Properties-as-meanings are abstracted from things, they are the properties-in-things as conceived and can be instantiated. The properties-in-thing are their instances or aspects inhering in their instances.

Now the properties-in-things can be really identical to the thing itself; in God's case all are. This guarantees God's simplicity without necessarily precluding positive theology. And even in case of God you can distinguish the property-as-in-God and the property-as-conceived. Due to the limitations of our intelect, individuality as such is never part of the property-as-conceived; in this sense all properties-as-conceived are universal, even if they happen to be necessarily exemplified but once. By saying that the divine nature is not a universal it is NOT JUST meant that it is only uniquely exemplifyable. It is meant that this "one common nature" is not a property-as-conceived, but a property-in-the-thing. That it is something real, whereas universals have merely intentional being, being-as-conceived.

Regarding the fact that there is no real distinction between God and his nature (meaning his real, individual nature): in my (and many a scholastic) theory this holds universally, not just for God. The nature is "made" a supposit by means of something called "suppositality", which in most cases is not regarded as really distinct from the nature itself (the distinction is taken to be of some lesser kind). Moreover, the "suppositality" canot be conceived as bringing some additional perfection or quidditative content to the nature. It is rather a kind of limitation or framing of the nature, inseparable from the nature itself.

Taking "common nature" to mean the nature-as-conceived, the question of its precise relation to God is IMHO irrelevant for the question of God's simplicity, because as such the nature is not something real, but merely intentional. Conceived as-in-things, no nature is common (meaning universal).

So: all aspects of divinity (properties-in-the-thing) are really identical to God, but they can be conceived separately, and thus univocal common concepts applying both to God and creatures result (e.g. "cause", "just", "being"). Unless we adopt some doctrine requiring some kind of distinction in reality between the various aspects of an object as an ontological sine qua non of the capability of these aspects of being separately conceived (like the scotist formal distinction), mere existence of universals aplicable to God doesn't seem to compromise divine simplicity.

AFAIK, the standard semantic background of the developed trinitarian doctrine (I mean, high and late scholasticism, 14th-17th century) was more or less the one described above, with some differences among the different schools (the Thomists insisting in rejecting univocity, e.g., etc.). But of course, many points would deserve much more detailed treatment, this was meant just as a rough explanation of points where it seemed to me that we misunerstood each other.

Best regards,

My suggestion is that the only way out for Trinitarians is to interpret the notion of "Person", not the notion of "God". See here:
1) The president John Fitzgerald Kennedy is a father
2) The president John Fitzgerald Kennedy is a son
3) The president John Fitzgerald Kennedy is a brother
4) To be a father is not the same role as to be a son
5) To be a son is not the same role as to be a brother
6) To be a brother is not the same role as to be a father
7) There is exactly one and only one president John Fitzgerald Kennedy

As Kennedy played several distinct roles at the same time,
God is playing three distinct roles at the same time.


Very good comment. That would solve the consistency problem since (1)-(7) is a consistent set of propositions. Unfortunately, it diverges from orthodoxy. Recall that one of the constraints on a solution was that it not fall into heresy. Your proposal seems close to Sabellian modalism.

Your idea is that the F, S, and HS are roles that God plays. The Persons are then *personae*, masks, of God. Are they then merely three different ways that God appears to us? That would be heterodox.

Suppose you say the Son is a role. What role? The role of Redeemer? But God qua Son cannot play the role of Redeemer unless there are creatures. But then God cannot be God without creating a world -- which is heterodox.

In orthodoxy, the Son is begotten (but not made) by the Father, and the HS proceeds from the Father and the Son. But this makes no sense if F, S, and HS are mere roles.

Dr Novak,

As I am sure you appreciate, much depends on one's background general ontology, and here we appear to have some disagreements. Perhaps I should write separate posts on our main points of disagreement.

You say 'being' is the highest genus. I've always maintained that it isn't.

You say "the properties-in-things can be really identical to the thing itself." I find that obscure. How could the individual essence Socrates' humanity beidentical to Socrates. Didn't youtell us that there is a suppositum in Socrates as well?


You say 'entity' is ambiguous. I see no ambiguity at all, or at least not the ambiguity you see. You write, >>It can either mean "a supposit", or "a being".<< To me that makes no sense. For me, an entity is a being, anything that is or exists. Everything is an entity, and there are no nonentities. For a nonentity would be nothing at all. Now I sometimes use the even more colorless and noncommittal term 'item' when I don't want to beg the question against Meinong and the Meioningians: they maintain that there are items that have no Being whatsoever: Der goldene Berg, zum Beispiel, ist jenseits von Sein und Nichtsein.

What I quoted you as saying above implies that a supposit is nothing at all. For if a supposit is not a being, then it is nothing at all.

There is a difference between ens and entitas, between a being and beingness. So one could say that 'entity' is ambiguous as between a being and beingness. But ordinarily in English we use 'entity' to refer to beings, not the beingness of beings. Using Heidegger's German we can draw a threefold distinction among das Seiende, die Seiendheit, und das Sein: that-which-is, beingness, and Being.

So we need to back up several steps if we are going to understand one another. So let's end this discussion for now, and resume it when I write separate posts on these different topics. Perhaps the first should be on whether being is a highest genus.

Lets count water! “Water?” Sort of…

Imagine we have a big bucket full of water. Call this bucket ‘G’. Suppose we also have three smaller buckets arranged in a specific order: call them ‘S1’, ‘S2’, and ‘S3’. It so happens that the volume of the small buckets equals the volume of G.

Regarding the amount of water in G we can legitimately say that it is exactly divisible into three amounts each of which will fill the smaller buckets. So the water in G has a certain potential to be divisible into three equal volumes each of which would fill the smaller buckets. I don't know whether we should call this a "dispositional property" or a "capacity" or whatever. Anyway, however we should label it, let us pour the water from G into S1, S2, and S3. Now G is empty and the water that was in G is now equally divided among the smaller buckets. We can legitimately say both that we now have three buckets of water and that we have exactly the same amount of water. We can also say that the water in each of the small buckets is exactly the same as a portion of the water that used to be in G. Which portion? Well, the portion that before was completely fused with the water in the other buckets. The water never changed. What changed is the manner in which it is contained. The first way, all the water was in G. The second way, the same exact water is now contained in three buckets rather than one. Thus, while the water is the same, the manner of containment is different. We can count water in two different ways: in terms of the manner it is contained or in terms of the quantity of water. If we count water in the manner it is contained, then we have two different counts: once we count in terms of the one container G and the second way is in terms of the three containers S1, S2, and S3. If we count water in terms of its quantity, then we always have the same quantity of water regardless whether the water is in container G or is divided into three smaller containers.

The reason we can do this is because water is a mass substance. Counting mass substances is not the same as counting individual objects that persist through time. The logic is different, as we have seen above. On the other hand, buckets are individual objects. There is nothing wrong with saying that in one way we have one bucket of water, whereas in another we have three and yet all along we have the same amount of water.

I suggest we try thinking about the Trinitarian doctrine along the same lines. I am sorry but I do not have the time presently to pursue it, but if others think it is a promising line of thinking, I invite them to do so. I may explore this idea in time.

By "role" I meant a parental role (like in the exemple of Kennedy): Kennedy can't be the president of USA without a country and a population, but he can be a father toward his children and son toward his parents.
Therefore the notion of "person" may correspond to the "parental role" that each person plays toward the other 2 persons of the trinity; so the role is not to be necessarily defined in relation to the world or the creatures.
The fact that the Father the Son and the Holy Ghost aren't made, could even make my proposal more appealing, because in that case I'm not in the embarrassing position of explaining how God can play three different roles at the same time by means of three acts of creation.
Even more, the fact that the Father begets the Son and the Holy Ghost proceeds from the Son and the Father just establishes a "parental" subordination between the three roles by definition, and that's all, such that it doesn't need to be explicated furtherly.
Perhaps I'm going a bit too far on that. In that case, forget it. But I'm not sure about what the orthodoxy considers heretical and what not. However it could still be a reasonable strategy to try to revise one heretical view and make it compliant with the orthodoxy.
One more question: are we sure that what we don't find possible is actually impossible? Think about the paradox of Achilles and the Tortoise. We could easily accept the premises, and deduce the conclusion that Achilles has to cover an infinite distance to reach the tortoise. But that's impossible! Nevertheless Achilles overtakes the Tortoise!

Pete, does the orthodoxy maintain that God is simple? If so, this analogy won't work either for if God is simple then he is not a whole divisible into parts, he has no extension, he has no mass quantity.



Lukas suggested above that in the classical (scholastic) texts „God“ can standardly have at least three senses:

(a) the divine nature (Godhead, divinity);
(b) a suppositum endowed with divine nature or „a supposit that is God“
(the Father, the Son, the Holy Ghost);
(c) the being having divine nature (the Holy Trinity).

As I understand Lukas, he has defended that it is not clear that every substantial being is numerically identical to some suppositum.

If every substantial being was numerically identical to some suppositum, then, arguably, God-(c) would be numerically identical to the Father; the same would hold for the Son and the Holy Ghost; and so these three would be numerically identical: which is against the doctrine of Trinity.

The Trinitarian can say that for any God-(b), God-(b) is a suppositum of God-(c) and God-(c) is a substantial being of suppositum God-(b).



Now, does Trinity entail Quaternity?, you recently asked in another post: http://maverickphilosopher.typepad.com/maverick_philosopher/2010/01/does-trinity-entail-quaternity.html Supposing the doctrine of Trinity, are there more than three (or even infinitely many) divine persons? Of course, one naturally asks, what do we mean here by „person“, and how is the concept of a person to be defined?

Suppose we do entertain an undefined, intuitive concept of a person when using the word „person“, and that Boethius‘s definition is a correct real (as opposed to nominal) definition of that concept: person =df substance of a rational nature. (I hope I‘ve got Boethius‘s definition right.)

Now, as Lukas suggested to me in our e-mail correspondence, „substance“ is in the classical literature ambiguous BTW at least two senses:
substantial being,

Accordingly, we have at least two Boethian definitions of person:
personA =df substantial being of a rational nature,
personB =df suppositum of a rational nature.

Given the doctrine of Trinity and the two Boethian definitions of person, God-(c) is a personA and any God-(b) is a personB. Thus, there is exactly one divine personA, and ther are exactly three divine personB‘s. So far, neither I see a metaphysical problem, nor I can derive any further divine personA or -B.


Way above in one of your responses to Dr. Novak, you said:

"I agree that the property of being an even prime has exactly one instance, the number 2. For this very reason, this property cannot be called universal. It is not a one over many, or a one in many. Universal = repeatable. Particular = unrepeatable."

But, now, consider the two apples on the table, the two chairs nearby, and all other pairs of items: Why can't we say that they are (in some sense) instances of the number 2? Or that they exemplify the property of being an even-prime number of items? There is of course only one *number* that is an even prime: But there may be many pairs of items all of which are an even prime number of things.

This is a problem. On the one hand, the number 2 is an individual. On the other, it can be repeatedly instantiated by any pair of items. So it is an individual when considered as a number, but is like a universal when considered with respect to all the pairs of items. What is it then?


Your proposal does seem to be close to modalism: i.e., modes of being, any version of which is apparently rejected by orthodoxy. I suppose it is time to make a provisional list of exactly what contradicts orthodoxy and in what senses.

Dear dr. Vallicella,

you mentioned 2 problems: the problem of the univocity of being, and the problem whether "entity" can be ambiguous or whether anything that is not a being is nothing. I would like to make two comments which I think may be useful even before you write regarding the other points.

Concerning the problem of univocity, I think it is not connected with the prolbem of Trinity. If you will, I can, for the sake of the discussion, assume that being is analogical, either in the Thomist (Cajetan's), or Suarezian sense (as you prefer :-)). I don't think it makes any difference in my argumentation. (I don't regard these theries as somehow inherently flawed, just unmotivated. Recently I have published a paper analyzing the problem of the cocnept of being, I can send an e-copy to you, in case you are interested).

On the other hand, what makes a huge difference is the latter problem. It seems to me that to define "being" as anything beside nothingness is very, very unhelpful. For it makes in effect impossible to to count beings in any objective way. It does not make sense to say "this is just one being" or "these are three beings". For any part of a being, any conceivable aspect of a being, any constitutive principle of a being and any aggregate of beings is certainly something "without nothingness", and yet you cannot say these are beings, without inducing manifold infinite regresses. For example, you cannot say that a nature (essence) is a being, for every being has its own essence, so every essence would have to have its own essence, etc. When you have a married couple, you can reasonably ask: how many beings are there? Is it just one being (the couple), or are they two beings? With your assumptions the question does not make sense, for the couple is a being, each member of the couple is a being, the left hand of each member is also a being, and so on.

Now in case of the Trinity the relation of the Persons to the Trinity is not that of parts to a whole; neverheless, the case is structurally similar. If you wish to give any meaningful numbers, you must specify numbers of WHAT you are giving. Saying "of whatever" (which in effect is tour menaing of "being") does not help, it makes the respective number essentially indetermined (any Person is "something", any couple of the Persons is "something", any couple of the couples, etc...).

But since this is maybe a merely terminological problem, I am prepared to give up the term "being" and I use the term "proper being" instead, meaning "an individual constituted by one individual essence (for the sake of simplicity, I am leaving aside necessary qualifications required to take the possibility of hypostatic union into question). This definition does not apply to parts, aggregates, or individual supposits sharing the same individual essence, without pushing them into the Outer Darkness of nothingness :-)

Nevertheless, I concede that the usage of "entity" (menaing "whatever (beside nothing)") in P1 is harmless, from this point of view, since the sort of what is counted is specified (God). Thus P1 is true if "God" means "divine nature" or "individual proper being of divine nature", and false if it means "a supposit of divine nature".

I hope this post of mine decreased and not increased the number of problems needing discussion... Now I promise I will wait till your replies are ready.

Best regards,



Are numbers properties or individuals? I see the problem you sketch. I don't have an answer at the moment.


We will have discuss these many issues in separate posts. You have already seen my post on whether being is a genus. Tomorrow I will publish something on supposita. I have read a lot of scholastic philosophy but I find the terminology very obscure.

Regards, and thanks for the discussion.

Let's consider these 3 notions "thick particular", "thin particular" and "sliced particular"
- a thin particular is an individual without all its properties
- a thick particular is an individual with all its properties
- a sliced particular is an individual with a proper subset of properties (where proper subset means neither empty nor containing all properties)
Let's apply these definitions to the example "Socrates is an athenian philosopher and father" (assuming that this is a complete description of Socrates)
- the thin particular would be Socrates without his properties, that is without the properties "being athenian" and "being a philosopher"
- the thick particular would be Socrates with all his properties, that is with the properties "being athenian", "being a philosopher" and "being a father"
- the sliced particular would be Socrates with the property of being athenian but also Socrates with the property of being a philosopher and Socrates with the property of being a philosopher and the property of being a father, etc...
Now let's consider the following questions, by considering the example above:
- How many thin particulars are there?... 1
- How many thick particulars are there?... 1
- How many sliced particulars are there?... 6 (that is "Socrates being athenian", "Socrates being a philosopher", and "Socrates being a father"; "Socrates being athenian and philosopher", "Socrates being athenian and a father", "Socrates being a father and a philosopher")
In principle we could further belabor the notion of "sliced particular" by adding and modifying constraints for example by saying that the proper subset of properties must be of cardinality one (in that case we would get only 3 sliced particular), or that the proper subset of properties must contain all and only the parental properties, where by the parental property is "being a father" (in that case we would have only 1 sliced particular). We should also note that a sliced particular is still a particular, it's not multi-instantiable.
How can we apply these notion to the trinity doctrine?
Let's assume that "God is divine, a father, a son and a holy ghost" is the full description of God
And let's define the notion of sliced particular as follow: an individual with the proper subset of properties which has the highest cardinality and contains only one p-property (where p-properties are by definition father, son and holy ghost). Now:
- How many thin particulars do we have?... 1
- How many thick particulars do we have?... 1
- How many sliced particulars do we have?... 3
The last step would be to rename that last notion of sliced particular as person and give a proper name to each person. Let's see what we have got here:
1) the Father is God (the Father is constituted by God as he is the individual thin particular of that person)
2) the Son is God (the Son is constituted by God as he is the individual thin particular of that person)
3) the Holy Ghost is God (Holy Ghost is constituted by God as he is the individual thin particular of that person)
4) the Father is not the Son (the Father is neither constituted by nor identical to the Son)
5) the Son is not the Holy Ghost (the Son is neither constituted by nor identical to the Holy Ghost)
6) the Holy Ghost is not the Father (the Holy Ghost is neither constituted by nor identical to the Father)
7) There is one and only one God (one and only thin particular and thick particular)
The conclusion is: 1 God in 3 Persons
Is this proposal feasible? If this approach certainly leads to heresy, I would be thankful if someone tells me exactly why, which assumptions apparently contradict what orthodox statements. Thanks


if I may express my view, your suggestion is not feasible, in the first place because your initial assumption is un-urthodox: namely that "divine, Father, Son, Holy Ghost" is a "full description of God". The personal characteristics cannot be taken as "properties of God", as though God were a subject of which they are predicated. It is quite the other way around: the Persons are the true subjects of which "God" is predicated.

You practically suggest that the Persons are some partial aspects of a single particular, God. This simply is not what is meant by "Persons" in the classical doctrine.

Best regards,


On the ontology of numbers I recommend this older post by Ed Buckner aka Ocham: http://ocham.blogspot.com/2008/06/did-god-create-all-things.html

Thanks a lot for your kind reply. I think that we are using different terminologies, and I don't know if you are considering that. Maybe this terminology need to be more detailed, but I don't want to get you bored, so in short:
- "Universal" = multi-instantiable
- "Particular" = not universal
- "Subject" = what predicates are ascribed to
- "Predicate" = what refers to properties
- "Thin particular" or "individual" = what remains of a state of affairs after we have removed all properties
- "Thick particular" = individual with all properties
- "Sliced particular" = individual with a proper subset of properties
- "Aspect" = proper subset of properties
- "Person" = an individual with the proper subset of properties which has the highest cardinality and contains only one p-property (where p-properties are by definition being a father, being a son and being a holy ghost)
- "the Father" = proper name denoting the person with "being a father"-property
- "the Son" = proper name denoting the person with "being a son"-property
- "the Holy Ghost" = proper name denoting the person with "being a holy ghost"-property
- "God" = proper name denoting an individual

According to these definitions then the definition of "Person" I've proposed meets the following requirements:
1) "Person" refers to a particular (not to a property as you say or an aspect)
2) "the Father" "the Son" "the Holy Ghost" and "God" are proper names
which refers to particulars
3) God is one particular in three particular and distinct Persons (if we interpret that "in" as a relation of constitution of God toward the 3 Persons)
4) Please note that I'm distinguishing "individual" from "particular": also a thick particular and a sliced particular are particulars!

I think that the main problem if we maintain the above terminology (which I guess would sound acceptable for an analytical ontologist) is that if you say:
"the Persons are the true subjects of which "God" is predicated"
means that the Persons would be the individuals and not just the particulars (according to my distinction) and God is a universal or multi-instantiable property by definition:
- Property because is predicated of
- Universal because the very same property is predicated of many individuals at the same time
And that would lead us straightforward to the issues raised by Bill, namely that there are 3 Gods.
Sorry for the length of the post. Regards


I think that the problem is not just terminology; the background ontology is different. For example, your definitions seem to identify a thick individual and a state of affairs. It seems to me to be a category mistake to conceive of states of affairs as somehow "made up" of individuals and properties. Also, what is it a property for you? It seems to me that your talk of "sliced particulars" presupposes that properties are always distinct from their bearers, whereas an "individual" seems to be like a peg on which any property can be hung. On this assumption any ascription of a property to God would imply God's non-simplicity, which is unacceptable from the orthodox point of view.

Your notion of "individual" is certainly different from the classical one, used to express the trinitarian doctrine. In the classical exposition of the doctrine, "individual" (not "particular") is the correlative of "universal". This is the sense to be understood when it is insisted that there is just one individual in God, just one individual instance of the universal Godhead. On the other hand, if you infer from "the Persons are the subjects" that "The persons are individuals", it seems (?) that you are using "individual" in a sense closer to the classical "supposit". To the same direction points also the (perhaps too vulgar) "peg" analogy. Thus it seems that your model for the Trinity has it actually reversed! :-) (But perhaps it would be useful for approaching the notion of the Hypostatic Union: one peg - the person of Christ - bearing two different individual properties - the natures divine and human.)

Trying to employ this idiom, the classical doctrine can perhaps be expressed this way: It does not deny that there are three individuals in your sense, or "pegs" for properties in God! Quite the contrary, it asserts that! The doctrine claims that there is just one individual instance of the property of godhead "hanging" simultaneously on the three pegs. Further it says that there is no real distinction betwen the property and the pegs: meaning that the godhead belongs to the inner constitution of the pegs.

But note that claiming real identity does not imply claiming numerical identity. The numerical identity always depends on what are you counting: whether pegs or the properties. It makes no sense to ask "is the Father numerically identical to God", because in order that two things can be numerically identical or distinct, they must have the same kind of numerical unity. But the numerical unity of God is different from that of a Person (cassically speaking, the former is a unity of an individual (as opposed to a universal), the latter is a unity of a supposit), therefore they cannot be compared with regard to the same kind of numerical identity/distinction.

Note also that the fact that one property hangs on three pegs does not imply that the property is a universal. A universal property is multiplied according to the number of pegs, Godhead is not. The classical denial that Godhead is universal only excludes its multiplication, not its hanging on three distinct pegs.

But maybe this is difficult to grasp for those who always view universal properties platonically as ALWAYS preserving their unity and not multiplying even when being hung on many distinct pegs/bare individuals. This is another reason why I am afraid that there is more than a terminological difference between yours and the classical account.

Well: I seem to write the longest posts here... I apologise...

Best regards!

I wrote above:

"As I understand Lukas, he has defended that it is not clear that every substantial being is numerically identical to some suppositum.

If every substantial being was numerically identical to some suppositum, then, arguably, God-(c) would be numerically identical to the Father; the same would hold for the Son and the Holy Ghost; and so these three would be numerically identical: which is against the doctrine of Trinity."

Lukas has written to me that "numerical identity" is for him ambiguous BTW:
numerical identity by which beings are counted, and
numerical identity by which supposita are counted.

So, his position is to be described rather as follows, and as Lukas has done already:
it is not clear that every substantial being has just one suppositum (where "has" is not meant to imply real non-identity of that which has from that which is had);
if every substantial being had just one suppositum, then the Father, the Son, and the Holy Ghost would not be three supposita, these three would be numerically identical: which is against the doctrine of Trinity.

Thanks to your reply I'm realizing that your ontological framework (which I will assume as orthodox) is pretty far from mine. Honestly your (or the orthodox) explanation of the trinity doctrine sounds to me even more puzzling than the minimal formulation of the trinity doctrine itself. But before going on with my perplexities, I'm wondering if there is a trivial error in your explanation. In fact in the same post you state:
1) This is the sense to be understood when it is insisted that there is just one individual in God, just one individual instance of the universal Godhead (that is: Godhead is universal)
2) A universal property is multiplied according to the number of pegs, Godhead is not (that is: Godhead is not universal)
One more question: you say that the Father, the Son and the Holy Ghost are what God "hangs on". Does that mean that the Father, the Son and the Holy Ghost are 3 distinct instances of God? Is the same kind of relation the one that connects God to a Person and Godhead to God?


I am sorry for the ambiguity. Please, do not take the "peg" speak too serious, it probably has more disadvantages than advantages.
Now: I used "Godhead" to mean two different things: 1) Godhead as a universal (if we allow universals with just one instance); 2) Godhead as the single instance of that universal. An analogy: Humanity vs. individual instance of humanity, say Socrates' humanity.

Now the point of the trinitary doctrine is that the Godhead common to the three Persons is not just a universal - like universal humanity common to many men -, but a singular entity. The persons are therefore NOT instances of Godhead (or of God). The individual Godhead, being the unique instance of the universal (sit venia verbo) Godhead, cannot be further instantiated. The relation of the individual Godhead to the Persons is not that of a universal being instantiated by several individuals, but that of an individual nature inhering simultaneously in three supposits.

An analogy: The relation of instantiation obtains between the universal "humanity" and its individual instances: Socrates' humanity, Plato's humanity, and so on. Or between the universal "man" and its instances: Socrates, Plato, etc. (See my comment to "Supposita" for the difference between "man" and "humanity").

The relation of inherence obtains between Socrates' humanity and Socrates. Here one individual nature (Socrates' humanity) inheres in one suppositum (Socrates). In God, there are three distinct supposita sharing one and the same individual nature.

So there is just one instance of Godhead, just one instance of God (whereas there are many instances of humanity and many instances of man). But this one instance of God subsists as three distinct supposita.

Best regards,

I have uploaded a scheme to help to get the basic idea of the relations between the individual nature, the suppositality/personality and the suppositum/supposita here:


The scheme is great. So much info in it.

In his last comments to Bill's post "Supposita," Lukas says that in (d)--(f), we have "is" of predication: e.g., the Son is God.

In my comments above, I used ""is" of predication," maybe non-standardly, to imply multiple instantiability and accidental (as opposed to substantial) ontological nature of that which is predicated (like in "Socrates is wise"), contra Lukas's use.

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